Home▸Statistics▸Statistical Sampling

Sampling Distribution & the Central Limit Theorem

Draw random samples from a skewed population and watch the histogram of sample means converge toward a normal bell curve — the Central Limit Theorem in action, with sample size and population shape tunable in real time.

Statistics2DEasy60 FPS📱 Mobile-adapted⇄ 3D version

Statistical analysis rests on being able to trust a sample mean as a stand-in for the whole population. This simulator draws repeated random samples from a population you choose — uniform, skewed, or bimodal — computes each sample's mean, and builds a live histogram of those means. Watch how, regardless of the population's own shape, the distribution of sample means converges toward a normal bell curve centered on the true population mean, and how increasing the sample size n narrows that curve according to the standard error σ/√n.

⚙ Under the hood

Repeatedly sample from a population and histogram the means to visualize the Central Limit Theorem.

statisticsprobabilitycentral limit theorem

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install